00000402.htm

INDEX 385

One-to-one mapping: 1.6

Onto mapping: 1.6

Open ball: 3.4

Open covering: 3.16

Open interval: 2.1

Open neighborhood: 3.6

Open polydisk: 9.1

Open set: 3.5

Operator: 11.1"'

Opposite path: 9.6

Order of an analytic function at a point:

9.15

Order of a linear differential operator: 8.13
Ordered pair: 1.3
Origin of an interval: 2.1
Origin of a path: 9.6
Orthogonal projection: 6.3
Orthogonal supplement: 6.3
Orthogonal system: 6.5
Orthogonal to a set (vector): 6.1
Orthogonal vectors: 6.1
Orthonormal system: 6.5
Orthonormalization: 6.6
Oscillation of a function: 3.14

Precompact set: 3.17
Precompact space: 3.16
Prehilbert space: 6.2
Primary factor: 9.12, prob. 1
Primitive: 8.7

Principle of analytic continuation: 9.4
Principle of extension of identities: 3.15
Principle of extension of inequalities: 3.15
Principle of isolated zeros: 9.1
Principle of maximum: 9.5
Product of a family of sets: 1.8
Product of metric spaces: 3.20
Product of normed spaces: 5.4
Projection (first, second, zth): 1.3
Projections in a direct sum: 5.4
Purely imaginary number: 4.4
Pythagoras's theorem: 6.2

Quasi-derivative, quasi-differentiable func-
tion: 8.4, prob. 4

Quasi-hermitian operator: 11.5, prob. 18
Quotient set: 1.8

^p-adic distance: 3.2

Parallel hyperplane: 5.8, prob. 3

Parseval's identities: 6.5

Partial derivative: 8.9

Partial mapping: 1.5

Partial sum (/zth) of a series: 5.2

Partition of a set: 1.8

Path: 9.6 and 10.2, prob. 6

Path reduced to a point: 9.6

Peano curve: 4.2, prob. 5, and 9.12, prob. 5

Peano's existence theorem: 10.5, prob. 4

Phragmen-Lindelofs principle: 9.5, prob.

Picard's theorem: 10.3, prob. 8
Piecewise linear function: 8.7 *

Point: 3.4

Pole of an analytic function: 9.15
Positive definite hermitian form: 6.2
Positive hermitian form: 6.2
Positive hermitian operator: 11,5
Positive number: 2.2
Power series: 9.1

Radii of a polydisk: 9.1

Radius of a ball: 3.4

Rational number: 2.2

Rank theorem: 10.3

Real line: 3.2

Real number: 2.1

Real part of a complex number: 4.4

Real vector space: 5.1

Reflexivity of a relation: 1.8

Regular frontier point for an analytic func-
tion: 9.15, prob. 7

Regular value for an operator: 11.1

Regularization: 8.12, prob. 2

Regulated function: 7.6

Relative maximum: 3.9, prob. 6

.. Relatively compact set':'3L*lT^

Remainder (nth) of a series: 5.2

Reproducing kernel: 6.3, prob. 4

Residue: 9.15

Resolvent of a linear differential equation:
10.8

Restriction of a mapping: 1.4

Riemann sums: 8.7, prob. 1



	INDEX 385

	One-to-one mapping: 1.6 Onto mapping: 1.6 Open ball: 3.4 Open covering: 3.16 Open interval: 2.1 Open neighborhood: 3.6 Open polydisk: 9.1 Open set: 3.5 Operator: 11.1"' Opposite path: 9.6 Order of an analytic function at a point: 9.15 Order of a linear differential operator: 8.13 Ordered pair: 1.3 Origin of an interval: 2.1 Origin of a path: 9.6 Orthogonal projection: 6.3 Orthogonal supplement: 6.3 Orthogonal system: 6.5 Orthogonal to a set (vector): 6.1 Orthogonal vectors: 6.1 Orthonormal system: 6.5 Orthonormalization: 6.6 Oscillation of a function: 3.14	Precompact set: 3.17 Precompact space: 3.16 Prehilbert space: 6.2 Primary factor: 9.12, prob. 1 Primitive: 8.7 Principle of analytic continuation: 9.4 Principle of extension of identities: 3.15 Principle of extension of inequalities: 3.15 Principle of isolated zeros: 9.1 Principle of maximum: 9.5 Product of a family of sets: 1.8 Product of metric spaces: 3.20 Product of normed spaces: 5.4 Projection (first, second, zth): 1.3 Projections in a direct sum: 5.4 Purely imaginary number: 4.4 Pythagoras's theorem: 6.2
		Quasi-derivative, quasi-differentiable func- tion: 8.4, prob. 4 Quasi-hermitian operator: 11.5, prob. 18 Quotient set: 1.8

	^p-adic distance: 3.2 Parallel hyperplane: 5.8, prob. 3 Parseval's identities: 6.5 Partial derivative: 8.9 Partial mapping: 1.5 Partial sum (/zth) of a series: 5.2 Partition of a set: 1.8 Path: 9.6 and 10.2, prob. 6 Path reduced to a point: 9.6 Peano curve: 4.2, prob. 5, and 9.12, prob. 5 Peano's existence theorem: 10.5, prob. 4 Phragmen-Lindelofs principle: 9.5, prob. 16 Picard's theorem: 10.3, prob. 8 Piecewise linear function: 8.7 * Point: 3.4 Pole of an analytic function: 9.15 Positive definite hermitian form: 6.2 Positive hermitian form: 6.2 Positive hermitian operator: 11,5 Positive number: 2.2 Power series: 9.1	Radii of a polydisk: 9.1 Radius of a ball: 3.4 Rational number: 2.2 Rank theorem: 10.3 Real line: 3.2 Real number: 2.1 Real part of a complex number: 4.4 Real vector space: 5.1 Reflexivity of a relation: 1.8 Regular frontier point for an analytic func- tion: 9.15, prob. 7 Regular value for an operator: 11.1 Regularization: 8.12, prob. 2 Regulated function: 7.6 Relative maximum: 3.9, prob. 6 .. Relatively compact set':'3LlT^ Remainder (nth)* of a series: 5.2 Reproducing kernel: 6.3, prob. 4 Residue: 9.15 Resolvent of a linear differential equation: 10.8 Restriction of a mapping: 1.4 Riemann sums: 8.7, prob. 1